﻿ 柔性立管阻力特性试验数据处理技术
 舰船科学技术  2021, Vol. 43 Issue (3): 88-94    DOI: 10.3404/j.issn.1672-7649.2021.03.018 PDF

1. 中国船舶及海洋工程设计研究所，上海 200011;
2. 上海交通大学 海洋工程国家重点实验室，上海 200240

An experimental data processing investigation of the drag force for a flexible riser
LI Man1, XU Yong-chao1, SHAN Tie-bing1, FU Shi-xiao2
1. Marine Design and Research Institute of China, Shanghai 200011, China;
2. State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200240, China
Abstract: In this paper, three different methods of experimental data processing are proposed to investigate the drag force for a flexible riser under uniform current. The steady bending deformation and strain are obtained by analyzing the deformation and vibration of the riser. Based on beam-bending theory, the deformation of the riser is described by a differential equation for the bending strain and drag force. A verification of the three methods is given by processing an example of strain with or without noise. The experimental data of tension and strain are processed differently by the three ways and the drag force are obtained finally.
Key words: flexible riser     steady bending deformation     drag force     data processing
0 引　言

1 柔性立管初始弯曲及微分方程 1.1 立管初始弯曲与轴向张力

 图 1 均匀来流下柔性立管初始弯曲 Fig. 1 Schematic of steady bending deformation of a flexible riser

 $\begin{split} \left[ {\varepsilon (z)} \right] &= \left[ {{A_1}}\quad{{A_2}} \quad \cdots\quad {{A_n}} \right]\times \\ &\quad{\left[ {\begin{array}{*{20}{c}} {\sin \left( {\dfrac{{\text{π}} }{L}{z_1}} \right)}&{\sin \left( {\dfrac{{2{\text{π}} }}{L}{z_1}} \right)}& \cdots &{\sin \left( {\dfrac{{n{\text{π}} }}{L}{z_1}} \right)} \\ {\sin \left( {\dfrac{{\text{π}} }{L}{z_2}} \right)}&{\sin \left( {\dfrac{{2{\text{π}}}}{L}{z_2}} \right)}& \cdots &{\sin \left( {\dfrac{{n{\text{π}}}}{L}{z_2}} \right)} \\ \vdots & \vdots & \ddots & \vdots \\ {\sin \left( {\dfrac{{\text{π}} }{L}{z_m}} \right)}&{\sin \left( {\dfrac{{2{\text{π}}}}{L}{z_m}} \right)}& \cdots &{\sin \left( {\dfrac{{n{\text{π}}}}{L}{z_m}} \right)} \end{array}} \right]^{\rm{T}}}_{n \times m} {\text{。}} \end{split}$ (12)

2.2 微段载荷分析法原理（DPP_2）

 图 6 立管表面微段作用力 Fig. 6 Schematic of the load on each micro segment of riser model

 $\begin{split} EI\frac{{{\partial ^2}\varepsilon (z)}}{{\partial {z^2}}} - \mathop T\limits^ - \varepsilon (z) = 0 , \\ \varepsilon {|_{z = 0}} = 0,\varepsilon {|_{z = {z_{js}}}} = \varepsilon ({z_{js}}) ,\\ \end{split}$ (13)

j段上满足方程：

 $\begin{split} EI\frac{{{\partial ^2}\varepsilon (z)}}{{\partial {z^2}}} - \mathop T\limits^ - \varepsilon (z) = {F_d}(j)R, \\ \varepsilon {|_{z = {z_{js}}}} = \varepsilon ({z_{js}}),\varepsilon {|_{z = ze}} = \varepsilon ({z_{je}}) , \\ \end{split}$ (14)

j段以后满足方程：

 $\begin{split} EI\frac{{{\partial ^2}\varepsilon (z)}}{{\partial {z^2}}} - \mathop T\limits^ - \varepsilon (z) = 0 ,\\ \varepsilon {|_{z = {z_{js}}}} = \varepsilon ({z_{js}}),\varepsilon {|_{z = L}} = 0 , \end{split}$ (15)

 $\begin{split} \frac{{\partial \varepsilon }}{{\partial z}}{|_{z = {z_{js - }}}} = \frac{{\partial \varepsilon }}{{\partial z}}{|_{z = {z_{js + }}}} ,\\ \frac{{\partial \varepsilon }}{{\partial z}}{|_{z = {z_{je - }}}} = \frac{{\partial \varepsilon }}{{\partial z}}{|_{z = {z_{je + }}}} ,\\ \end{split}$ (16)

 ${\varepsilon _{ij}} = {R_{ij}}{F_d}(j),$ (17)

 $\begin{split} {\varepsilon _i} = \sum\limits_{j = 1}^m {{\varepsilon _{ij}}} = &\left[ {\begin{array}{*{20}{c}} {{F_d}(1)}&{{F_d}(2)}& \cdots &{{F_d}(m)} \end{array}} \right],\\[-8pt] &{\left[ {\begin{array}{*{20}{c}} {{R_{i1}}}&{{R_{i2}}}& \cdots &{{R_{im}}} \end{array}} \right]^{\rm{T}}} ,\end{split}$ (18)

 $\begin{split}\left[ {\varepsilon (z)} \right] = & \left[ {\begin{array}{*{20}{c}} {{F_d}(1)}&{{F_d}(2)}& \cdots &{{F_d}(m)} \end{array}} \right]\times\\ &{\left[ {\begin{array}{*{20}{c}} {{R_{11}}}&{{R_{12}}}& \cdots &{{R_{1m}}} \\ {{R_{21}}}&{{R_{22}}}& \cdots &{{R_{2m}}} \\ \vdots & \vdots & \ddots & \vdots \\ {{R_{m1}}}&{{R_{m2}}}& \cdots &{{R_{mm}}} \end{array}} \right]^{\rm{T}}}_{m \times m}{\text{。}}\end{split}$ (19)

2.3 逼近分析法原理（DPP_3）

 \begin{aligned}&\left[ {\varepsilon ({z_1}),\varepsilon ({z_2}), \cdots\varepsilon ({z_m})} \right] =\\ &{F_{d1}}\left[ {\begin{array}{*{20}{c}} {{R_{1d1}}}&{{R_{2d1}}}& \cdots &{{R_{md1}}} \end{array}} \right],\end{aligned} (20)

$\Delta 1\_\varepsilon =\left[ {\varepsilon ({z_1}),\varepsilon ({z_2}),\cdots\varepsilon ({z_m})} \right]-{F_{d1}} \left[ {{R_{1d1}}}\;{{R_{2d1}}}\cdots {{R_{md1}}} \right]$ 为一次差。显然如果阻力均匀分布，那么一次差 $\Delta 1\_\varepsilon$ 接近为0，反之则 $\Delta 1\_\varepsilon$ 不为0。若 $\Delta 1\_\varepsilon$ 不为0，可以假设立管在前1/2与后1/2上的阻力分别是均布的，对应的阻力分别为 ${F_{d21}}$ ${F_{d22}}$ ，其在坐标 ${z_i}$ 处的弯曲应变为：

 ${\varepsilon _i} = {R_{id21}}{F_{d21}} + {R_{id22}}{F_{d22}},$ (21)

 $\left[ {\Delta 1\_\varepsilon (z)} \right] = \left[ {{F_{d21}}}\quad {{F_{d22}}} \right]\left[ {\begin{array}{*{20}{c}} {{R_{1d21}}}&{{R_{2d21}}}& \cdots &{{R_{md21}}} \\ {{R_{1d22}}}&{{R_{2d22}}}& \cdots &{{R_{md22}}} \end{array}} \right]\text{。}$ (22)

 ${F_{di}} = {F_{d{2^{n - 1}}i}} + {F_{d{2^{n - 2}}rup(i/2)}} + {F_{d{2^{n - 3}}rup(i/4)}} + \cdots + {F_{d1}},$ (23)

2.4 算例与分析

2）流速越大，流体阻力越大。流体阻力沿着立管大致均匀分布，流体阻力沿立管中点大致对称，两端的流体阻力比中间区域大。圆柱绕流的数值计算表明，有限长圆柱两端的阻力比中间区域阻力大[4]，称为端面效应。柔性立管的两端同样存在端面效应，即两端阻力较中间大。

4 结　语

1）微段载荷分析法对噪声敏感，其分析结果与其他两种结果的比较可用来判断应变信号是否良好。模态分析方法和逼近分析法有较好的抗噪声能力。模态分析法结果不能准确预报立管各截面出的阻力系数，平均阻力的计算结果较准确。逼近分析法由于避免了求导的过程，且根据立管表面漩涡脱落特性进行假设分析，因此其结果可大体上显示出立管表面阻力的分布特性。

2）由于立管两端的流场特性与中部不同，导致立管端面的流体的阻力比中间的部分大。逼近分析法的结果显示了立管表面流体阻力分布的端面效应。

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